We prove the existence of a ground state solution for the following fractional scalar field equation $$ (-\Delta)^{s} u= g(u) \mbox{ in } \mathbb{R}^{N} $$ where $s\in (0, 1)$, $N>2s$, $(-\Delta)^{s}$ is the fractional Laplacian, and $g\in C^{1, \beta}(\mathbb{R}, \mathbb{R})$ is an odd function satisfying the critical growth assumption.
Ground states for a fractional scalar field problem with critical growth / Ambrosio, Vincenzo. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - 30:1-2(2017), pp. 115-132.
Ground states for a fractional scalar field problem with critical growth
Ambrosio, Vincenzo
2017-01-01
Abstract
We prove the existence of a ground state solution for the following fractional scalar field equation $$ (-\Delta)^{s} u= g(u) \mbox{ in } \mathbb{R}^{N} $$ where $s\in (0, 1)$, $N>2s$, $(-\Delta)^{s}$ is the fractional Laplacian, and $g\in C^{1, \beta}(\mathbb{R}, \mathbb{R})$ is an odd function satisfying the critical growth assumption.File in questo prodotto:
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